The invention relates to a method of MR (=magnetic resonance) imaging, wherein, using a gradient system, a magnetic field Bgrad that is variable over time and space is used for the spatial selection of a region to be imaged and for at least two-dimensional spatial encoding of the MR signals in the region to be imaged of an object to be examined, wherein the magnetic field Bgrad has nlin field components with a spatially linear and nnonlin field components with a spatially non-linear dependence, wherein nlin+nnonlin≧1 and nlin, nnonlinεN, wherein the amplitude and the spatial dependence of Bgrad are controlled by means of the strength and the ratio of the amplitudes of the individual field components, wherein the RF (=radio frequency) pulse(s) is/are transmitted by an RF transmitter system with nS transmitter coils, where nSεN and nS≧1 and wherein the RF signal transmitted by the object to be examined is received by an RF receiver system with nE receiver coils, where nEεN and nE≧1.
Partial aspects of such a method are known, for example, from [1] and [2].
Magnetic resonance imaging is a non-invasive method for the spatial resolution and display of the internal structure of an object, for example, the human body. The method is based on the energy behavior of atomic nuclei in an external magnetic field, which permits excitation of the nuclear spins by means of suitable RF (=radio frequency) pulses, as well as subsequent read-out of the signals emitted by the excited nuclear spins.
The received MR signal is composed of the individual signals of all the excited spins. Spatial allocation of these signals requires that the positions of the spins be encoded in advance, during the acquisition (recording) process. For this, spatially variable magnetic fields Bgradi(x,y,z) are superposed on the main magnetic field B0. According to equation {1}, this results in a space-dependent variation of the Larmor frequency νL of the atomic nuclei, where B(x,y,z) designates the magnitude of the resulting magnetic field and γ, the gyromagnetic ratio:νL(x,y,z)=B(x,y,z)/γ  {1}
Conventionally, spatial encoding is achieved using superimposed magnetic fields, termed linear gradients, in which the change of field strength in space is as linear as possible. To produce these by linear combination, gradient systems are available with three field components whose linear gradients are aligned along the x-, y-, and z-axes and are therefore orthogonal with respect to one another. Spatial encoding in either one, two, or three dimensions is performed by varying the amplitude of the gradients in the relevant spatial directions according to the known principles, either by Fourier encoding, filtered back projection, or another known method [3].
If a superimposed magnetic field (Bgrad1) is produced during irradiation of the RF pulse, spatial delimitation of the excited volume results. In this process, termed slice selection, only those nuclear spins are excited whose Larmor frequency νL is within the bandwidth of the RF pulse. When conventional linear slice selection gradients are used, the selected volume has the typical shape of a planar slice. This is fully defined via its flat midsurface AM whereBgrad1(AM)=γ*frequency offset  {2}and its thickness, wherein the latter derives from the amplitude of the superimposed magnetic field and the bandwidth of the RF pulse. The normal of the midsurface is always aligned parallel with the linear gradient of the superimposed magnetic field Bgrad1. Because the latter is produced by linear combination from a set of field components with orthogonal gradients, it can be put together to produce any orientation and positioning of the slice. The orthogonality of the gradients also enables the production of further superimposed magnetic fields Bgradi, whose gradients are perpendicular with respect to one another and with respect to the midsurface normal, and consequently ensures spatial encoding along the midsurface of the excited slice. This corresponds to a standard projection of the spin density that is perpendicular to the midsurface and therefore to a rectangular voxel volume.
The MR signal read out for the different variations of the superimposed magnetic fields is allocated to so-called k-space, wherein the position in k-space results from the strength, duration, and orientation of the switched superimposed magnetic fields. The order in which k-space points are sampled during recording is described by the trajectory of the acquisition method used. Generally, the signal components containing low-frequency information and therefore the approximate structure of the object to be mapped are encoded at the center of k-space, while the edge regions contain detailed, the higher-frequency information. The size of the field of view FOV (=Field of View) of the resulting MR image is proportional to the sampling density 1/Δk of k-space. If the FOV is too small and does not entirely cover the object to be imaged, the outer regions of the object to be imaged appear folded inward in the reconstructed MR image. These folded image components are termed aliasing.
In the case of one-dimensional acquisition, only one row in k-space has to be acquired. The superimposed magnetic field switched during acquisition is termed the read-out gradient. For a given sampling density, the resolution of an MR acquisition is therefore determined by the strength and duration of the read-out gradient. The steeper the gradient and the longer it is switched, the further from the center of k-space are the acquired points. For a two-dimensional MR acquisition, multiple k-space rows are acquired, wherein the number of rows corresponds to the number of points in the second dimension of the image. The superimposed magnetic field (“phase gradient”) responsible for the so-called phase encoding is switched for a certain time interval between excitation and acquisition of the signal, wherein the gradient strength is varied accordingly for each row. The acquisition duration therefore results from the product of the number of rows and the duration TR (=Time of Repetition) for acquisition of one row. In the case of a three-dimensional MR acquisition, k-space is extended by a third dimension; for encoding, an additional phase gradient is switched in the relevant direction. The number of k-space points along each dimension, and therefore also the number of resulting voxels, is described by the matrix size. In the case of a matrix size of Nx×Ny×Nz and row acquisition duration TR, a total acquisition time TA (=Time of Acquisition):TA(3D)=Ny×Nz×TR therefore results for a 3D-acquisition,  {3}and correspondingly, for a 2D-acquisition with an Nx×Ny matrix:TA(2D)=Ny×TR.  {4}
In the usual case of an equidistantly sampled k-space, the signal density in frequency space is calculated directly by means of the iFT (=inverse Fourier transform) of the k-space signal. The subsequent transformation of the signal density into real space results from the respective spatial dependence of the superimposed magnetic field used for encoding.
One established possibility for reducing the acquisition duration is to use several receiver coils and the resulting spatial information [4]. In the parallel imaging technique SENSE [5, 6], specific k-space rows are omitted during acquisition. The acquisition duration is shortened; this is referred to as acceleration. The MR images reconstructed from the data acquired by the individual coils are however folded as a result of the reduced sampling density. Because of the varying spatial sensitivity of the individual receiver coils with which each received signal is modulated, different weighting arises in each coil image between the intensity of the image and the intensity of the aliasing caused by folding. If the sensitivity distributions of the individual coils are known, the aliasing can be described by solving a corresponding system of equations and calculated accordingly from the overall image resulting from all coil data. A further parallel imaging technique is known as GRAPPA [7, 8]: Unlike SENSE, in this case, the missing k-space rows are calculated from the additional coil information before reconstruction of the MR image.
Standard MR imaging techniques use purely linear gradient systems and permit the mapping of thin slices in any orientation and with a rectangular voxel shape. However, because of the linearity of the gradients, it is limited to the selection and encoding of planar slices. Organic structures such as are found in the spinal canal or on the surface of the brain, in particular, cannot be described by a planar slice. Complete coverage of such structures therefore necessitates the selection of a thick slice, combined with the time-consuming three-dimensional encoding or acquisition of multiple planes followed by reformatting of the individual slices. The selection and encoding of a curved slice whose shape can be adapted to the structure of the object to be examined is therefore desirable.
As early as 1989, Lee and Cho [9] demonstrated that, by using a superimposed magnetic field of shape Bgrad1=x2±y2−2z2, application of a superimposed magnetic field with a spatially non-linear dependence as the slice selection gradient permits selection of a volume that deviates from the shape of a planar slice. In this method developed for two-dimensional limitation of the selection volume, the excited, cylindrical volume was subsequently spatially resolved by time-consuming linear 3D-encoding. Oh and colleagues [1] expanded this technique by applying an additional linear gradient during irradiation of an RF refocusing pulse, so that the 3D-encoding of the cylindrical volume could be reduced to the 2D-encoding of a planar, circular slice. In further work, they [10], and Wu and colleagues [11], also demonstrated that the selection volume can be spatially shifted during the selection process by the additional application of magnetic field components with a spatially linear dependence, and that the shape of the selection volume can be altered by varying the frequency offset of the RF pulse. These early methods explicitly aim at selection of a planar slice, albeit spatially limited.
As an alternative to choosing the selection volume via the spatial dependence of the slice selection gradient, in 1996, Börnert and Schäffter [12, 13] demonstrated that the selection process can be spatially delimited using mufti-dimensional RF pulses. The selection of curved slices, whose position, orientation, and curvature can be very flexibly chosen was also explicitly demonstrated. The spatially selective excitation using mufti-dimensional RF pulses is based on irradiation of an RF pulse with a temporal dependence adapted to the shape of the volume to be selected combined with a spatially and temporally variable amplitude and orientation of the superimposed magnetic field Bgrad1. The sequence of switching, including the strength, duration, and orientation of the superimposed magnetic field Bgrad1 is described analogously with switching of the superimposed magnetic fields for spatial encoding by a corresponding trajectory in the (transmission) k-space. Here, too, the spatial extent of the region in which the volume to be selected is to be located is proportional to the sampling density, the resolution of the target pattern of the volume to be selected and also proportional to the number of sampling points of transmission k-space. To allow additional selective excitation along the third dimension, the transmitter k-space must be extended accordingly. Because the entire trajectory is sampled during a single transmission of the RF pulse, resolution of the target sample is usually severely restricted by the strength and switching rate of the superimposed magnetic field Bgrad1 as well as the dephasing rate of the signal already excited. The longer duration of multi-dimensional RF pulses as compared with conventional, one-dimensional RF pulses increases the minimum possible echo time of the acquisitions. It additionally results in an increased sensitivity with respect to the inhomogeneities of the static magnetic field, which above all results in non-homogeneous excitation and artifacts. Moreover, the energy requirement of RF pulses, which increases with the dimension, results in a large increase in the energy deposition in the object to be examined even with two-dimensional RF pulses. SAR (specific absorption rate) limits therefore impose restrictions on the choice of pulse and thus on the slice shape. Selection by means of multi-dimensional RF pulses is therefore considerably more complex than with conventional, one-dimensional pulses and their practical application is severely limited in some cases.
Börnert and Schäffter have also demonstrated the problems associated with spatial encoding of a curved slice. Conventional encoding with linear gradients corresponds to projection of the non-planar slice onto a planar surface. The orthogonality criterion, which states that encoding gradients and surface normal must be mutually perpendicular, can therefore only be met in a few regions. The more the midsurface normal of the excited slice deviates from this, the more distorted the shape of the resulting voxel will be. This is accompanied by a reduction in the local resolution and even ambiguities if the spin densities of different regions coincide spatially. This is the case, for example, if a slice curved with an angular bend of more than 90° is projected onto a plane. To be able to separate regions superposed during projection despite this, Börnert and Schäffter [13] propose additional RF encoding of the relevant regions. In a further development of this method with refined regions, Börnert [14] demonstrates an approximation to a slice curved along the slice dimension by concatenation of N rectangular voxels of the same orientation. Encoding along the voxel chain is achieved by N-fold excitation of the voxel chain, wherein the phase is varied along the voxel chain by appropriate adaptation of the 2D RF pulse. Based on known principles, such as the Fourier transform, the voxels can subsequently be separated again. The method thus reduces the two-dimensionality of the reconstruction to one dimension. One disadvantage of this method is that, due to the nature of the method, during RF pulse encoding of a curved slice, the typical problems occur that are associated with the use of multi-dimensional pulses, such as great sensitivity to inhomogeneities of the static magnetic field or increased energy deposition in the object to be examined. Moreover, multiple irradiation of complex RF pulses means that the method is also susceptible to individual disturbances of the pulses. The resulting irregularities in encoding along the voxel chain result, for example, in intensity modulation or disturbance signals. Even if the method can theoretically be applied to encoding along both slice dimensions of a curved slice, it is limited to one curved dimension in practice: besides the problem of 3D RF pulses already mentioned, encoding an N×N “voxel carpet” would result in an N-fold increase in the acquisition duration. Moreover, although the voxels have a rectangular shape, their lateral surfaces are not usually aligned with the midsurface.
In particular, the aforementioned problem of reduced local resolution persists. Encoding along the curved slice for projection of the spin density perpendicular to its midsurface is therefore not possible with this method.
An alternative approach for encoding a slice selected with 2D RF pulses and curved along a slice dimension was proposed by Jochimsen and colleagues [15]. In their method, an approximation to the curved midsurface of the slice is achieved with multiple planes. A plane in three-dimensional k-space can be allocated to each of these planes. The k-space points are defined taking into account the sampling density necessitated by the resolution. Reconstruction along the curved slice is performed by means of numeric Fourier-integration. The main disadvantage of this method concerns the requirements with regard to slice shape: it can only be curved along one dimension and approximation to the curve by means of a polygon must be possible. The method also assumes that the contrast along the midsurface normal is constant for every point in the slice, since interference may otherwise occur between the individual planes. Moreover, every plane must be fully sampled to avoid aliasing. Because of the superposition of the individual segments, more points are therefore acquired than would be required for reconstruction of the actual curved slice. This inefficiency increases with the number of segments. In practice, only rough approximation of encoding along the curved slice can be achieved by this method.
The object of the invention is therefore to provide an MR imaging method with which curved slices can be mapped efficiently and with high resolution. The method should be adapted to the respective slice shape.